Statistical Theory and Modelling
1st Edition
Published on 1. November 1990
Book
Hardback
376 pages
978-0-412-30590-0 (ISBN)
Description
Statistical Theory and Modelling is a celebration of the work of Sir David Cox, FRS, and reflects his many interests in statistical theory and methods. It is a series of review articles, intended as an introduction to a variety of topics suitable for the graduate student and practicing statistician. Many of the topics are the subject of book-length treatments by Sir David and authors of this volume. Each chapter leads to a larger literature.
Topics range the breadth of statistics and include modern degvelopments in statistical theory and methods. Special topics covered are generalized linear models, residuals and diagnostics, survival analysis, sequential analysis, time series, stochastic modelling of spatial data, design of experiments, likelihood inference and statistical approximation.
Topics range the breadth of statistics and include modern degvelopments in statistical theory and methods. Special topics covered are generalized linear models, residuals and diagnostics, survival analysis, sequential analysis, time series, stochastic modelling of spatial data, design of experiments, likelihood inference and statistical approximation.
More details
Language
English
Place of publication
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Professional and scholarly
Weight
608 gr
ISBN-13
978-0-412-30590-0 (9780412305900)
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Schweitzer Classification
Persons
Content
Part 1 Statistical theory - theoretical concepts; significance tests; theory of optimal tests; estimation; asymptotic theory. Part 2 Applied statistics - preliminary considerations; statistical models; statistical inference; model adequancy; exploratory and robust methods; multi-variate methods; use of computers. Part 3 Generalized linear models - a class of non-linear regression models; likelihood functions; estimation; analysis of deviance; checking the model. Part 4 Residuals and diagnostics - general remarks; normal theory linear model; a general definition; general regression models. Part 5 Life table analysis - survival distributions; inference for a single sample; dependence on explanatory variables; inference for models involving explanatory variables; graphical methods - goodness of fit; several types of failure: competing risks; multi-variate failure distributions. Part 6 Sequential methods - Wald's theory of the SPRT; sequential tests with nuisance parameters; sequential estimation; sequential clinical trials; decision theory and optimality in clinical trials; inference and decisions; sequential design and related topics. Part 7 Time series methods - stationary models; frequency domain; parametric models; non-parametric estimation; regression with correlated errors. Part 8 Modelling stochastic phenomena - independence and the Markov property; semi-Markov and Markov renewal processes; point processes; spatial processes; applications. Part 9 Optimal design of experiments - convex design theory; numerical methods; some specific designs for standard problems; non-standard problems. Part 10 Likelihood theory - the primary theory; some refinements; pseudo-likelihoods. Part 11 Quasi-likelihood and estimating functions - least squares; quasi-likelihood estimation; quasi-likelihood function; estimating functions; confidence sets; an open problem. Part 12 Approximations and asymptotics - basic theory and notation; edgeworth expansion; saddlepoint expansion; Laplace approximations; stochastic asymptotic expansion.